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Simplifying 6m2 = 23m + 15 Reorder the terms: 6m2 = 15 + 23m Solving 6m2 = 15 + 23m Solving for variable 'm'. Reorder the terms: -15 + -23m + 6m2 = 15 + 23m + -15 + -23m Reorder the terms: -15 + -23m + 6m2 = 15 + -15 + 23m + -23m Combine like terms: 15 + -15 = 0 -15 + -23m + 6m2 = 0 + 23m + -23m -15 + -23m + 6m2 = 23m + -23m Combine like terms: 23m + -23m = 0 -15 + -23m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + -3.833333333m + m2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.833333333m + 2.5 + m2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.833333333m + m2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.833333333m + m2 = 0 + 2.5 -3.833333333m + m2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.833333333m + m2 = 2.5 The m term is -3.833333333m. Take half its coefficient (-1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. -3.833333333m + 3.673611112 + m2 = 2.5 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333m + m2 = 2.5 + 3.673611112 Combine like terms: 2.5 + 3.673611112 = 6.173611112 3.673611112 + -3.833333333m + m2 = 6.173611112 Factor a perfect square on the left side: (m + -1.916666667)(m + -1.916666667) = 6.173611112 Calculate the square root of the right side: 2.484675253 Break this problem into two subproblems by setting (m + -1.916666667) equal to 2.484675253 and -2.484675253.Subproblem 1
m + -1.916666667 = 2.484675253 Simplifying m + -1.916666667 = 2.484675253 Reorder the terms: -1.916666667 + m = 2.484675253 Solving -1.916666667 + m = 2.484675253 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + m = 2.484675253 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + m = 2.484675253 + 1.916666667 m = 2.484675253 + 1.916666667 Combine like terms: 2.484675253 + 1.916666667 = 4.40134192 m = 4.40134192 Simplifying m = 4.40134192Subproblem 2
m + -1.916666667 = -2.484675253 Simplifying m + -1.916666667 = -2.484675253 Reorder the terms: -1.916666667 + m = -2.484675253 Solving -1.916666667 + m = -2.484675253 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + m = -2.484675253 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + m = -2.484675253 + 1.916666667 m = -2.484675253 + 1.916666667 Combine like terms: -2.484675253 + 1.916666667 = -0.568008586 m = -0.568008586 Simplifying m = -0.568008586Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.40134192, -0.568008586}
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